Collisionless relaxation in non-neutral plasmas

A theoretical framework is presented which allows to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particles beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a core-halo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.Comment: Accepted in Phys. Rev. Let

Temperature inversion in long-range interacting systems

Temperature inversions occur in nature, e.g., in the solar corona and in interstellar molecular clouds: somewhat counterintuitively, denser parts of the system are colder than dilute ones. We propose a simple and appealing way to spontaneously generate temperature inversions in systems with long-range interactions, by preparing them in inhomogeneous thermal equilibrium states and then applying an impulsive perturbation. In similar situations, short-range systems would typically relax to another thermal equilibrium, with uniform temperature profile. By contrast, in long-range systems, the interplay between wave-particle interaction and spatial inhomogeneity drives the system to nonequilibrium stationary states that generically exhibit temperature inversion. We demonstrate this mechanism in a simple mean-field model and in a two-dimensional self-gravitating system. Our work underlines the crucial role the range of interparticle interaction plays in determining the nature of steady states out of thermal equilibrium.Comment: 5 pages + 6 pages of appendix, 5 figures, REVTeX 4-1. To appear in Physical Review E (Rapid Communications). Appendix will be published online-only as Supplemental Materia

Emittance growth and halo formation in the relaxation of mismatched beams

In this paper, a simplified theoretical model that allows prediction of the final stationary state attained by an initially mismatched beam is presented. The proposed stationary state has a core-halo distribution. Based on the incompressibility of the Vlasov phase-space dynamics, the core behaves as a completely degenerate Fermi gas, where the particles occupy the lowest possible energy states accessible to them. On the other hand, the halo is given by a tenuous uniform distribution that extends up to a maximum energy determined by the core-particle resonance. This leads to a self-consistent model in which the beam density and self-fields can be determined analytically. The theory allows one to estimate the emittance growth and the fraction of particles that evaporate to the halo in the relaxation process. Self-consistent N-particle simulation results are also presented and are used to verify the theory

Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings

We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams. \ua9 2014 American Physical Society